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¹H NMR: Long-Range Coupling01:27

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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sp3d and sp3d 2 Hybridization
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than...
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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Synergy between pair coupled cluster doubles and pair density functional theory.

Alejandro J Garza1, Ireneusz W Bulik1, Thomas M Henderson2

  • 1Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA.

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|February 2, 2015
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Pair coupled cluster doubles (pCCD) methods now include dynamic correlation by blending with density functionals. This approach enhances accuracy for complex chemical problems with minimal computational cost.

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Area of Science:

  • Quantum chemistry
  • Computational physics

Background:

  • Pair coupled cluster doubles (pCCD) accounts for static correlation at low cost.
  • Static and dynamic electron correlation are crucial for accurate chemical predictions.
  • Existing methods struggle to balance accuracy and computational expense for these correlations.

Purpose of the Study:

  • To develop and evaluate new computational methods combining pCCD with density functional theory (DFT).
  • To incorporate dynamic correlation into pCCD without introducing double counting.
  • To improve the description of chemical systems requiring both static and dynamic correlation.

Main Methods:

  • Combining pair coupled cluster doubles (pCCD) with Kohn-Sham functionals.
  • Utilizing on-top pair density functionals to capture dynamic correlation.
  • Developing pCCD+DFT blends with minimal computational overhead.

Main Results:

  • The pCCD+DFT blends significantly improve upon pCCD for systems with both static and dynamic correlation.
  • The computational cost increase for the pCCD+DFT blends is negligible.
  • The enhanced methods provide a more accurate description of challenging chemical problems.

Conclusions:

  • pCCD is well-suited for integration with pair density functionals due to its favorable properties.
  • pCCD+DFT blends offer a promising, computationally efficient approach for multireference problems.
  • This fusion method enhances the capabilities of pCCD for describing complex electronic structures.